Abstract:

For reliability evaluation of the life following Weibull distribution under Type I censoring test plan with small sample size,it is discovered on the basis of Monte Carlo simulations that the ratio of the median of the shape parameter moment  estimation and the true value of the shape parameter depends only on the sample size and the failure number while neither on the shape parameter nor the scale parameter,
under the assumption that the failure number is in accordance with the arbitrary time in
 the corresponding time interval.Based on this,a median unbiased moment
estimation method was proposed,and the values of the bias correcting factor for the sample sizes
of 2~12 were provided.Further,the proposed method was compared with moment
estimation method through numerical analysis,and the results show that the former
performs significantly better than the latter,taking median bias and RMSE
(root mean square error) as evaluation criteria.Finally,practicality,validity and superiority of the proposed method were verified by conducting two tests.

Key words: Weibull distribution, reliability evaluation, Monte Carlo simulation, median unbiased moment estimation

摘要：

针对Weibull分布产品小样本定时截尾试验方案下的可靠性评估问题，假设样本结构在截尾时间为使该样本结构出现概率最大的截尾时间区间内的任意一点时产生，应用Monte Carlo模拟方法,发现形状参数矩估计量中值与其真值之比值仅取决于样本结构,而不受分布母体影响，据此提出了中值无偏矩估计法，并给出了2~12样本量的中值无偏系数取值。以偏差和均方根误差为评价指标，通过数值模拟方法，对该方法和矩估计法进行比较后发现，在两项指标上，前者较后者均具有明显优势。通过试验验证了所提出方法的实用性、有效性和优越性。

关键词: Weibull分布, 可靠性评估, Monte Carlo模拟, 中值无偏矩估计